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Marbles Bonanza (Posted on 2003-09-08) Difficulty: 4 of 5
You have an empty container, and an infinite number of marbles, each numbered with an integer from 1 to infinity.

At the start of the minute, you put marbles 1 - 10 into the container, then remove one of the marbles and throw it away. You do this again after 30 seconds, then again in 15 seconds, and again in 7.5 seconds. You continuosly repeat this process, each time after half as long an interval as the time before, until the minute is over.

Since this means that you repeated the process an infinite number of times, you have "processed" all your marbles.

How many marbles are in the container at the end of the minute if for every repetition (numbered N)

A. You remove the marble numbered (10 * N)

B. You remove the marble numbered (N)

See The Solution Submitted by levik    
Rating: 3.6154 (13 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Interestingly | Comment 4 of 83 |
I think all those below solutions are correct, so I won't repeat, but interestingly in A you have exactly the same number of marbles inside the jar as outside, since you can make an exact one-to-one match with each pair of marbles -
1 -> 10
2 -> 20
and so on. This is the case even though at first glance it looks like you have nine times as many marbles in the jar as out.
Edited on September 8, 2003, 10:26 pm
  Posted by sam on 2003-09-08 22:24:34
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